Page 1 of 1

FALL 2013 ASSIGNMENT

PROGRAM BACHELOR OF COMPUTER APPLICATION

SEMESTER 5TH SEM

SUBJECT CODE & NAME

BC0052 – THEORY OF COMPUTER SCIENCE

CREDIT 4

BK ID B0972

MAX. MARKS 60

Answer all Questions

Q.No Questions Marks Total Marks

1 Define g.c.d. (m,n)

Solve recursively: (i) f(x, y) = x + y

(ii) g(x, 0) = 0, g(x, y + 1) = g(x, y) + x.

[3+3.5+3.5]

10

2 Obtain a DFA to accept strings of a’s and b’s starting with the string ab.

[10] 10

3 Prove by mathematical induction

6

)12)(1(.......321 2222

nnn

n

[10] 10

4 Briefly describe Moore and Mealy machines. [10] 10

5 If )},,10{},1,0{},({ SSSSSG then find L(G),

the language generated by G.

[10] 10

6 Prove that “A tree G with n vertices has (n–1) edges” [10] 10